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To find the interquartile range (IQR) of the data set {4, 3, 4, 1, 6}, we follow these steps:

### 1. Sort the Data:
First, we sort the data in ascending order:
\[
1, 3, 4, 4, 6
\]

### 2. Identify Quartiles:
- **Q1 (First Quartile)**: The median of the lower half (excluding the overall median if there's an odd number of data points). The lower half is {1, 3}, so \( Q1 = 3 \).
- **Q3 (Third Quartile)**: The median of the upper half (excluding the overall median if there's an odd number of data points). The upper half is {4, 6}, so \( Q3 = 4 \).

### 3. Calculate the Interquartile Range (IQR):
The IQR is the difference between the third quartile and the first quartile:
\[
\text{IQR} = Q3 - Q1 = 4 - 3 = 1
\]

Thus, the interquartile range is **1**.

Would you like any further details or clarifications?

### Related Questions:
1. What is the range of this data set?
2. How do you calculate the median for an even-numbered data set?
3. Why is the interquartile range useful for measuring spread?
4. How does the interquartile range differ from standard deviation?
5. What happens if the data set contains outliers?

**Tip**: The interquartile range is resistant to outliers, making it a robust measure of variability.

In the data set below, what is the interquartile range? Data set: 4, 3, 4, 1, 6

Learn how to calculate the interquartile range (IQR) for the data set {4, 3, 4, 1, 6}. This problem involves sorting the data, finding Q1 and Q3, and applying the IQR formula. Suitable for students in Grades 6-8.

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